Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+x=12
-
Equation (-2x+1)*(-2x-7)=0
- Equation x-y+1=0
-
Equation 9x+4=48-2x
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -5*x-2*y=9
-
Identical expressions
- x^ two - seven *x- thirty = zero
- x squared minus 7 multiply by x minus 30 equally 0
- x to the power of two minus seven multiply by x minus thirty equally zero
- x2-7*x-30=0
- x²-7*x-30=0
- x to the power of 2-7*x-30=0
- x^2-7x-30=0
- x2-7x-30=0
- x^2-7*x-30=O
-
Similar expressions
- x^2-7*x+30=0
- x^2+7*x-30=0
x^2-7*x-30=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = -30$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = -3$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = -30$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (1) * (-30) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = -30$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = -30$$
Sum and product of roots
[src]
sum
-3 + 10
$$-3 + 10$$
=
7
$$7$$
product
-3*10
$$- 30$$
=
-30
$$-30$$
-30
The graph